J. Phys. Chem. B 1998, 102, 1071-1076
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ARTICLES Spin Exchange of Cation Radicals in Solid Polymeric Matrixes Deanna Hurum, Brad Bovenzi, and Robert W. Kreilick* Department of Chemistry, UniVersity of Rochester, Rochester, New York 14627
David Weiss Office Imaging Research and Technology Department, Eastman Kodak Company, Rochester, New York 14650 ReceiVed: June 30, 1997
We have used EPR spectroscopy to determine the rate of spin exchange between cation radicals held in rigid polymeric matrixes. Radicals of this type are thought to be the charge carriers during electrophotographic conduction. A variety of diamagnetic compounds were added to these samples to examine the idea of “superexchange” which was proposed in earlier work. Diamagnetic tertiary amines are proposed as conduits for spin exchange in the “superexchange” mechanism. This work shows that this mechanism is incorrect. We also demonstrate how measurement of exchange energies can be used to find relative separations of radicals held in the polymeric matrixes.
Introduction The charge generation and charge transport materials widely used in electrophotographic copiers are generally aromatic organic compounds that are readily oxidized or reduced to radical ions.1 These molecules are held in thin (15-50 µm) layers of various types of polymers in random but rigid orientations. A bilayer, with charge generation molecules in a relatively thin layer and charge transport molecules in a second relatively thick layer, is employed as the photoreceptor. Typical molecules used for charge generation are derivatives of perylene or phthalocyanines while typical charge transport molecules are tertiary amines such as tritolylamine (TTA). The tertiary amine is oxidized to its cation radical, and conduction is dependent on the rate of hole migration to the negative electrode. Hole drift mobility increases with increased TTA concentration and is presumed to depend on overlap of the wave functions of adjacent TTA molecules. Earlier work has suggested that hole mobility2,3 is also related to the rate of spin exchange observed from stable amine cation radicals which are held in a polymeric matrix. The rate of spin exchange measured by EPR spectroscopy was found to depend on both the concentration of the cation radical and the concentration of neutral TTA. There have been numerous reports of spin exchange in solution where rate of spin exchange is generally diffusion controlled4 but fewer investigations in the solid state.5 In the solid state the exchange rate depends on relative separation and geometry of radicals. The rate of spin exchange has been found to have an exponential dependence on the separation of the radicals as shown in eq 1,6,7
J ) J0e-(R - R0/R0) * To whom correspondence
[email protected]).
should
(1) be
addressed
(e-mail:
where J is the observed exchange energy when the radicals are separated by a distance R and J0 is the exchange energy when the radicals are at a minimum separation R0. The rate of spin exchange of charged radical salts held in polymeric solids is found to depend on both the concentration of radical salt and the concentration of the neutral precursor of the radical cation.2 The dependence of the exchange rate on the concentration of neutral TTA has previously been explained by a superexchange mechanism by Troup et al.2 The superexchange mechanism involves participation of the π system of the neutral TTA molecules in the exchange process. The π system serves as a type of conduit for transfer of spin states between radical cations separated by TTA molecules. This paper describes an investigation of spin exchange between TTA•+ molecules in a series of polymeric matrixes. A series of diamagnetic diluents were added to the radical-polymer matrixes to determine their effect on spin exchange. This work shows that the superexchange mechanism proposed by Troup et al. is not a significant mechanism for the observed spin exchange in this system. The study also demonstrates that one can determine the relative separation of radicals within the polymeric matrixes. Experimental Section a. Materials. The polycarbonate (PC) (Makrolon, 95% polycarbonate A, 5% polycarbonate Z, MW 197 000) (ref 1; Appendix 1, p 414) was purchased from Mobay Chemical. The polyester (PE)(T60C-GJ, MW 128 728) (ref 1, Appendix 1, p 415) was supplied by Eastman Kodak. Polystyrene (PS, MW 280 000) was purchased from Aldrich. Tritolylamine was obtained from Eastman Kodak research labs, and Cambridge Isotopes prepared the perdeuterotritolylamine (dTTA). Tris(bromophenyl)amine (TBPA), triphenylmethane (TPM), and tricyclohexylmethane (TCM) were obtained from Aldrich. The TBPA was recrystallized from ethanol in the absence of light
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TABLE 1: Coupling Constants (MHz) of TTA•+SbCl5AN(x,y)
AN(z)
AN (iso)
Amethyl (iso)
Aortho (iso)
Ameta (iso)
6.5
66.5
26.65
10.89
5.77
2.88
and was stored in the dark. A solution of 1 M antimony pentachloride in methylene chloride was also purchased from Aldrich chemical. The cation radicals of the amines were made using the antimony pentachloride solution by the method of Wieland.8 b. Films. Thin films of the doped PC samples were hand coated on glass or polyethylene-coated paper (from Felix Schoeller Co.) using a 5 mil coating blade and were approximately 20-30 µm thick. The approximate thicknesses of the dry films were determined from the wet thickness of the film and the volume percent of solids in the wet solution. Stock solutions of about 5 wt % of polymer in methylene chloride were produced. Appropriate weights of TTA•+SbCl5- and neutral compounds were added to the stock solutions of polymers to provide samples of the desired composition. c. Instrumental. EPR spectra were acquired on a Bruker ER200D-SRC X-band spectrometer. The concentration of the radical salt within the polycarbonate films was determined by UV-vis immediately following the EPR experiments to compensate for any decomposition of the radical which may have occurred during the coating of the film. The molar extinction coefficient for TTA•+SbCl5- in methylene chloride was determined to be 23 200 cm/M through studies of solutions of known concentration confirmed by EPR spin counting. This value agrees well with the extinction coefficient found for the electrochemically generated TTA cation radical in acetonitrile.9 d. Density Measurements. The densities of the polymer films were determined by a suspension method.9 A sample of film was submerged in a vial of water. Potassium iodide was then added to the water until the film rose off the bottom of the vial to the middle of the column of solution. After suspension of the film occurred, a 1 mL sample of the solution was pipeted out and weighed. The density of the solution corresponds to the density of the film. The solution was regularly purged with helium to prevent air bubbles from adhering to the film and lifting it to the surface. Due to the large surface area of the films, small air bubbles were particularly troublesome and the densities determined are not highly accurate but allow for comparison of the densities of the samples in this work. e. Determination of Spin Exchange Rates. Dynamic processes which affect NMR, EPR, or ENDOR line shapes are often accounted for through use of the modified Bloch equations.10 When three or fewer different magnetic sites are interchanged, analytical solutions for these equations are easily found and solved to produce theoretical line shapes. In cases in which multiple magnetic sites are interchanged, it is difficult to find an analytical solution and one must solve a large set of simultaneous equations. In general, if n sites are interchanged, one must solve n simultaneous equations. Alternatively, these equations can be represented by an n × n matrix of the coefficients of the complex magnetization. Solving the matrix at a series of magnetic field values which encompass the experimental spectrum provides the theoretical line shape. A faster method developed by Reeves11 involves rearrangement of the matrix equations so that the problem can be solved by diagonalization of a single n × n matrix at each field value. Even with this technique, the array size for a system with a large number of magnetic sites is often too large to be solved with the matrix routines available on a personal computer. We have developed a method through which this problem can be simplified further for cases in which the lifetime of all
of the states is identical. This treatment shows that all matrix operations can be replaced by multiplication and division of various matrix elements. This approach reduces computational time and allows one to simulate spectra for systems with large numbers of magnetic sites with a personal computer. This technique is particularly valuable for simulation of EPR spectra in systems in which spin exchange affects the line shape. All nuclear spin states must be used to obtain accurate simulations and the size of the exchange matrix may exceed 2000 × 2000 in cases in which a large number of nuclear spins are coupled to the electron. In the case of the TTA cation, 1473 energy levels must be included in the calculation while 9633 levels must be included for deuterated TTA cation radical. The derivation of equations used for analysis of spectra to determine exchange rates is given in the Supporting Information. The equation used to simulate EPR spectra to determine exchange rates is given by
([ ] [ ]) n
-ip1/d1 c [-ipn/dn] -ip2/d2 n)1 ‚ n ‚ 1 + c 1/dn -ipn/dn
∑
G B)
∑
n)1
1/d1 1/d2 ‚ ‚ 1/dn
(2)
In this equation, pn is related to the intensity of line n and dn is given by
dn )
[(
)
]
1 1 1 + - i∆ωn + T2 τ τ(N - 1)
(3)
in which τ is the lifetime of a given spin state and equal to 1/J; the observed exchange frequency. T2 is the spin-spin relaxation time in the absence of exchange, ∆ω is the offset from resonance, and N is the number of nuclear spin energy levels. Equation 2 describes the complex magnetization (G), which gives the overall line shape in an exchanging system. Results and Discussion Analysis of EPR line shapes to determine exchange rates requires knowledge of the isotropic and anisotropic coupling constants for the TTA•+SbCl5- radical. The values for the anisotropic nitrogen hyperfine constants and g-values were determined from a sample of dTTA•+SbCl5- doped into a polycarbonate film. Proton hyperfine coupling constants have previously been reported 12 and were substantiated through simulation of a solution spectrum of TTA•+SbCl5-. The g values and hyperfine coupling constants determined for our samples are listed in Table 1 and were used in the simulations of the EPR spectra of TTA•+SbCl5- doped films. Typical experimental and simulated EPR spectra of TTA•+SbCl5- in polycarbonate at various concentrations are shown in Figure 1. The concentration dependence of the exchange rate was measured for three types of polymers. A plot of the dependence of exchange frequency on the weight percent of the TTA•+SbCl5- radical salt in these polymers is shown in Figure 2. The exchange frequencies determined in PC and PE matrixes were nearly identical, while the exchange energy in PS was almost a factor of 5 higher for a given concentration of radical. If the polymers act as ideal solutions in which the cation radical is dissolved, then all of the samples should show the same concentration dependence of the exchange rate. These results indicate that the relative separation between radicals in the polar PC and PE polymeric matrixes differs from that of radicals in the comparatively nonpolar PS matrix. The charged cation radical and its anion are solvated more readily
Cation Radicals in Solid Polymeric Matrixes
J. Phys. Chem. B, Vol. 102, No. 7, 1998 1073
Figure 1. Experimental and simulated EPR spectra of PC films containing increasing weight percent of TTA•+SbCl5- in polycarbonate films.
Figure 3. Exchange frequencies versus weight percent of TTA•+SbCl5in polycarbonate films doped with neutral TTA: (0) ) films doped with a 1:14 radical to TTA mole ratio; (4) films doped with a 1:5 radical to TTA mole ratio; (+) films doped with a 1:1 radical to TTA mole ratio; (O) films doped only with the radical salt.
experiments which showed an increase of the exchange rate on addition of neutral TTA were explained by a superexchange mechanism. Our experimental data indicate that the superexchange mechanism is incorrect for this polymer system. The experiments are best explained by a mechanism in which the addition of neutral molecules changes the average radicalradical separation which directly determines the exchange rate. We repeated experiments similar to Troup’s in which samples with a constant mole ratio of TTA•+SbCl5- to neutral TTA were made in a PC matrix.
% (w/w) radical salt ) TTA•+SbCl5-
Figure 2. Exchange frequencies versus weight percent in various polymers: (O) polystyrene films; (0) polyester films; (3) polycarbonate films.
by the polar polymers and dispersed at larger average distances than cation radicals in PS. It should be emphasized that the polymeric solutions are microscopically homogeneous from the perspective of the cation radicals. If the radical salt precipitated from the polymer, the EPR spectrum would show the sharp exchange narrowed line from microcrystals of the radical molecules. Spectral simulations show that microcrystalline regions could be detected from samples in which less than 0.5% of the radical precipitated from the polymer. The continuous change in the EPR line shape with radical concentration and the lack of observable microcrystals show that each of the samples investigated are microscopically homogeneous. We have investigated the effect of the addition of neutral molecules to the radical-polymer mixture in some detail to determine the mechanism through which the neutral molecules affect the rate of spin exchange in these systems. Previous
wt radical salt (4) wt radical salt + wt neutral + wt polymer Three series of samples were made with different cation/neutral ratios and the exchange rates were compared to those in which only TTA•+SbCl5- was added to the polymeric matrix. The samples were made with mole ratios of 1:1 radical:neutral, 1:5 radical:neutral, and 1:14 radical:neutral. With these series, the exchange rate at a single concentration of radical salt per weight of film could be determined as a function of neutral concentrations. As in Troup’s work, the exchange rate for a given concentration of radical increased as the concentration of neutral amine increased. The large differences in the rates can be seen in the plots in Figure 3. Here the exchange frequency (J), as determined from simulation of EPR spectra, is plotted against the weight percent of TTA•+SbCl5- in the film as defined in eq 4. These data show that addition of the neutral amine directly influences the rate of spin exchange of TTA•+SbCl5- radicals held in the polymeric matrix. For a given concentration of the TTA•+SbCl5- radical, the rate of spin exchange increases as the amount of neutral TTA is increased.
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Figure 4. Representation of the appearance of doped polycarbonate films as the films are allowed to crystallize.
The increase in the rate of spin exchange with increased concentration of neutral TTA has been explained by a superexchange mechanism. This type of mechanism involves the π system of neutral TTA molecules acting as a conduit for transmission of spin polarization between TTA•+SbCl5- radicals separated by one or more neutral TTA molecules. The neutral TTA molecules could in principle be momentarily oxidized to radicals as the spin diffused through the samples. To test this hypothetical mechanism for long-range spin exchange, we conducted experiments in which various neutral materials were used to dilute the polymer mixture. The first molecule chosen was tris(bromophenyl)amine (TBPA) which has a similar structure to TTA but a higher oxidation potential (0.3 V).12 If superexchange involved oxidation of adjacent neutral molecules, the rate of spin exchange should be slower with this molecule than with TTA due to the higher oxidation potential. The rates of spin exchange with TTA and TBPA as diluents were found to be almost identical. If the superexchange mechanism requires only an adjacent π system for transfer of spin polarization, one might be able to rationalize the results from TBPA. To check this hypothesis, samples were made in which triphenylmethane (TPM) was used to dilute the radical polymer mixture. TPM has a much higher oxidation potential than either amine but has a π system and is similar in shape and size to TTA. The rate of spin exchange was enhanced a similar amount by addition of TPM as it was by TTA or TBPA. A final set of experiments involved dilution of the radical polymer mixtures with tricyclohexylmethanol. This is an unconjugated molecule which is similar in shape and size to TTA but should not serve as a conduit for spin exchange because it has no π system. The results obtained upon dilution with this molecule were similar to those with TTA, TBPA, and TPM showing that the observed enhancement in the rate of spin exchange does not depend on the neutral diluent molecule type and is unlikely to be due to a superexchange mechanism through the different molecules. An alternative explanation of these experimental observations is that addition of neutral molecules to the radical polymer mixture does not dilute the charged radicals but instead systematically concentrates the radicals in a different region of the polymer. With this model, charged cation radicals and their associated anion would concentrate in one microscopic region of the polymeric matrix (region 1) while the neutral diluent molecules would concentrate in a second region (region 2). As the concentration of neutral molecules is increased the volume of region 2 would increase and the volume of region 1 would decrease, forcing the charged radicals closer together and increasing the rate of spin exchange.
Figure 5. Relative radical separations versus weight percent TTA•+SbCl5- in polycarbonate films doped with neutral TTA: (0) films doped with a 1:14 radical to TTA mole ratio; (4) films doped with a 1:5 radical to TTA mole ratio; (+) films doped with a 1:1 radical to TTA mole ratio; (O) films doped only with radical.
The TTA•+SbCl5- radical and neutral TTA are almost insoluble in each other. Attempts to cocrystallize TTA•+SbCl5and neutral TTA resulted in less than 1% incorporation of the radical in neutral TTA. Evaporation of a methylene chloride solution of the two compounds resulted in a mixed solid in which the blue radical could be physically separated from the white TTA. A small amount of TTA was incorporated in the TTA•+SbCl5- as confirmed by EPR. Taking into consideration that the two compounds do not cocrystallize, it is not unreasonable that the radical and neutral molecules prefer to remain in different regions of the polymeric matrix when methylene chloride is removed from the mixture of radical, neutral TTA, and polymer. To confirm the inhomogeneous composition in these polymeric mixtures we attempted differential scanning calorimetry experiments. Unfortunately, the radicals decomposed near the glass transition temperature of the polymer mixtures. We also conducted experiments in which the amorphous films were allowed to crystallize through exposure to methylene chloride vapor.13 Crystallization of the polymer could be confirmed through use of FTIR spectroscopy to follow the carbonyl band which shifted from 1775 to 1769 cm-1 as the film crystallized.14 The amorphous polymer films of each sample visually appeared homogeneous before exposure to methylene chloride. After the mixed films of TTA, TTA•+SbCl5-, and polymer were allowed to crystallize, separate dark blue and nearly colorless regions were observed. The films doped only with TTA•+SbCl5- did not show any visible inhomogeneity after solvent-induced crystallization. The mixed films are clearly not homogeneous after solvent-induced crystallization as the color and EPR spectra show that the TTA and TTA•+SbCl5- have collected in different regions of the film. A schematic of this behavior is shown in Figure 4. The EPR spectra of the films show that the rate of
Cation Radicals in Solid Polymeric Matrixes
Figure 6. Relative radical separations versus weight percent TTA•+SbCl5- in polycarbonate films doped with various neutral molecules: (0) films doped with a 1:12 radical to TBPA mole ratio; (4) films doped with a 1:9 radical to TPM mole ratio; (]) ) films doped with a 1:10 radical to TCM mole ratio; (O) films doped only with radical. The inset in the upper right shows an expansion of the curves from samples doped with neutral molecules to show the small differences in slopes.
spin exchange has increased only slightly relative to the original cast amorphous film. The EPR data shows that the spin exchange behavior of the film before and after crystallization is nearly identical, while visually the film now appears quite inhomogeneous. This indicates the initial film is unlikely to be homogeneous. If the observed separate regions of radical cation and TTA were caused by the crystallization of the polymer, the EPR of the two samples would be different. The exchange frequencies measured by EPR allow one to estimate the average separation of the radicals in the polymeric host (eq 1). We assumed that R0 could be approximated by the nitrogen-nitrogen separation of 4.59 Å found in X-ray structure of TTA.15 J0 is given by the exchange rate in pure samples of TTA•+SbCl5- (3000 MHz). Figures 5 and 6 show plots of the concentration dependence of the average radical separation for the various samples. Figure 5 contains data for samples diluted with TTA while Figure 6 contains data for the other diluents. These plots clearly show that as TTA•+SbCl5in a polycarbonate matrix is diluted with a neutral diluent, the average distance between the radicals decreases. When neutral diluents are added to the radical-polymer mixture, the curve is displaced so that for a given radical concentration, the radical-radical separation is decreased. These results also provide an explanation of the change in drift mobilities of mixed TTA•+SbCl5-/TTA samples.3 The drift mobilities were found to increase as TTA•+SbCl5- was added to a sample of TTA. This result is consistent with regions of TTA in the polymer in which the separation of TTA molecules is decreased and hole migration is more effective. To verify that the changes in distance are not due to packing differences within a polymer of constant volume, we measured
J. Phys. Chem. B, Vol. 102, No. 7, 1998 1075
Figure 7. Slopes (radical separations/weight percent TTA•+) of lines from Figures 5 and 6 versus mole ratio of diluent to radical: 1, radical only, 2, 1:1 mole ratio TTA to TTA•+; 3, 4.7:1 mole ratio TTA to TTA•+; 4, 9:1 mole ratio TPM to TTA•+, 5, 10:1 mole ratio TCM to TTA•+; 6, 12:1 mole ratio TBPA to TTA•+; 7, 14:1 mole ratio TTA to TTA•+.
the density of the various samples using the suspension method described earlier. The density remained between 1.2 and 1.4 g/cm3 for all of the samples, indicating a linear expansion in volume as the polymer was loaded with the TTA and the more dense TTA•+SbCl5-. Density measurements of thin films of this type are not highly accurate but we should have been able to measure the large change in density if the samples had not increased volume as material was dissolved in the polymer. The films increase in volume, indicating that the decrease of distances between the radicals is not due to packing limitations of the polymer. If one takes the slopes (effective distance/wt % radical) of each of the curves in Figures 5 and 6 and plots them against the mole fraction (diluent/radical) one observes the plot given in Figure 7. This figure shows that each of the neutral diluents used in this investigation has a very similar effect on the radical-radical separation. This data supports the idea that neutral molecules displace the charged molecules to different regions in the polymeric matrix. If the chemical properties of the compounds were important, the data would be dependent on the neutral molecule. Experiments were also conducted with a neutral nitroxide free radical (2,2,6,6-tetramethyl-4-hydroxypiperidine-1-oxy (Tempol)). Films containing only Tempol and polycarbonate as well as mixed films with Tempol, TPM, and polycarbonate were made. Contrary to the radical salt data, the rate of spin exchange decreased when TPM was added to the radical polymer samples. In this case, the neutral radical and TPM do not segregate in the polymer and addition of TPM dilutes the radical. This dilution causes the Tempol-Tempol separation to becomes larger, and correspondingly the rate of spin exchange decreases.
1076 J. Phys. Chem. B, Vol. 102, No. 7, 1998 Conclusions Experiments have determined that the measured the rate of spin exchange between TTA•+SbCl5- cations depends on the type of polymeric host and the addition of neutral diluent molecules. The idea that a neutral diluent can act as a conduit for superexchange has been shown to be unlikely for this system. The cation radical and neutral diluent molecules appear to occupy different regions of the polymeric matrix leading to a decrease in separation of cation radicals and increase in exchange frequency as the diluent concentration is increased. Conversely, the separation between the TTA neutral molecules is also decreased by the addition of TTA cation radical salt, causing the previously observed increase in the conductivity of the films. Acknowledgment. The authors acknowledge Jeff Astheimer for valuable contributions to the mathematical formalism and financial support from NIH grant GM-22793 and NSF grant CHE-9120001. References and Notes (1) Borsenberger, P. M.; Weiss, D. S. Organic Photoreceptors for Imaging Systems; Marcel Dekker: Inc., New York, 1993.
Hurum et al. (2) Troup, A.; Mort, J.; Grammatica, S.; Sandman, D. J. Solid State Commun. 1980, 33, 91. (3) Troup, A.; Mort, J.; Grammatica, S.; Sandman, D. J. J. Non-Cryst. Solids 1980, 35-36, 151. (4) Berliner, L. J. Spin Labeling Theory and Applications; Academic Press: New York, 1976. (5) Pake, G. E.; Estle, T. L. The Physical Principles of Electron Paramagnetic Resonance, 2nd ed.; W. A. Benjamin, Inc.: Reading, MA, 1973. (6) Mao, C. R.; Kreilick, R. W. Mol. Phys. 1976, 31, 1447. (7) Zhou, D.; Kreilick, R. J. Phys. Chem. 1993, 97, 9304. (8) Wieland, H. Chem. Ber. 1907, 40, 4260. (9) Gould, I.; Ege, D.; Moser, J. E.; Farid, S. J. Am. Chem. Soc. 1990, 112, 4290. (10) Sandstrom, J. Dynamic NMR Spectroscopy; Academic Press: New York, 1982. (11) Reeves, L. W.; Shaw, K. N. Can. J. Chem. 1970, 48, 364. (12) Seo, E. T.; Nelson, R. F.; Fritsch, J. M..; Marcoux, L. S.; Leedy, D. W.; Adams, R. N. J. Am. Chem. Soc. 1966, 88, 3498. (13) Rebenfeld, L.; Makarewicz, P. J.; Weigmann, H.; Wilkes, G. L. J. Macromol Sci.sReV Macromol. Chem. 1976, C15, 279. (14) Varnell, D. F.; Runt, J. P.; Coleman M. M. Macromolecules 1981, 14, 1350. (15) Reynolds, S. L.; Scaringe, R. P. Cryst. Struct. Commun. 1982, 11, 1129. (16) McConnell, H. J. Chem. Phys. 1958, 28, 430.
